Sage 1 can only guess for one case:
- when ?BB can be seen, Sage 1 must have W. (Note: if this happened, Sage 2 would see W?B, and Sage 3 would see WB?)
- otherwise, Sage 1 must pass.

Sage 2 can guess for two cases:
- when B?B can be seen, Sage 2 must have W. (Note: if this happened, Sage 3 would see BW?)
- when W?B can be seen, Sage 2 must have W, otherwise Sage 1 would have seen ?BB and guessed. (Note: if this happened, Sage 3 would see WW?)
- otherwise, Sage 2 must pass.

Sage 3 will always know:
- when BB? can be seen, Sage 3 must have W.
- when BW? can be seen, Sage 3 must have W, otherwise Sage 2 would have seen B?B and guessed.
- when WB? or WW? can be seen, Sage 3 must have W, otherwise one of the other sages would have guessed.